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From |
[email protected] (Jeff Pitblado, StataCorp LP) |

To |
[email protected] |

Subject |
Re: st: Interacting continuous variable with a factor variable using c. as the prefix for the continuous variable |

Date |
Fri, 08 Jan 2010 15:13:11 -0600 |

Thomas Weichle <[email protected]> is interacting a continuous variable with a factor (indicator) variable using the '#' and '##' operators, and asks why the model fits are different: > I'm trying to create an interaction with a continuous variable and a > factor variable using c. as the prefix for the continuous variable. How > come I receive different results when using the following model syntax? > I understand that some of the output interpretations are slightly > different but things like the log likelihood, LR chi2, and degrees of > freedom should be the same. > > Model 1: > stcox chemo#c.income > > Model 2: > stcox chemo##c.income > > Model 2 is equivalent to the following model: > gen chemo_income = chemo*income > stcox chemo income chemo_income > > Model 1 contains exactly 1 less degree of freedom. It is not clear to > me why Model 1 and Model 2 aren't equivalent. > > I was able to demonstrate that when interacting 2 factor variables the > following models would be equivalent: > stcox chemo#male > stcox chemo##male > > However, I'm having a hard time showing the equivalency of interacting a > continuous and factor variable. Let's use the auto data, interacting -foreign- (a 0-1 indicator variable) with -turn-, so that our example somewhat lines up with Thomas'. The only other difference is that we'll use -regress- instead of -stcox-. . sysuse auto . gen dt = (foreign==0) * turn . gen ft = (foreign==1) * turn The basic model fits are: (1) . regress mpg for#c.turn and (2) . regress mpg for##c.turn Model (1) is equivalent to . regress mpg dt ft and Model (2) is equivalent to . regress mpg foreign turn dt ft The only difference between these two models is the inclusion of the main effect of -foreign- in Model (2). We could take -turn- out of Model (2) without affecting the model fit because -turn- is collinear with -dt- and -ft-; in fact since -turn, -dt-, and -ft- are collinear we can remove any one of them from the model without affecting the model fit (we can look at the MSE and linear predictions to verify this). -foreign- is not collinear with any other variable in Model (1), thus including it in Model (2) yields a difference model fit. Now when we change the model to be the interaction between two factor variables, such as -foreign- and -rep78-; we see that (3) . regress mpg for#rep and (4) . regress mpg for##rep yield equivalent model fits. This is because -foreign- is collinear with the level variables in -for#rep-, and so is -rep78-. --Jeff [email protected] * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: Behavior of tsrevar in Stata & Mata***From:*"Schaffer, Mark E" <[email protected]>

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